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Quantum one-time programs

A "one-time program" for a channel C is a
hypothetical cryptographic primitive by which a user may evaluate C on only one
input state of her choice. (Think Mission Impossible: "this tape
will self-destruct in five seconds.") One-time programs cannot be
achieved without extra assumptions such as secure hardware; it is known that
one-time programs can be constructed for classical channels using a very basic
hypothetical hardware device called a "one-time memory".

Our main result is the construction of a one-time program
for any quantum channel specified by a circuit, assuming the same basic
one-time memory devices used for classical channels. The construction
achieves universal composability -- the strongest possible security -- against
any quantum adversary. It employs a technique for computation on
authenticated quantum data and we present a new authentication scheme called
the "trap" scheme for this purpose.

Finally, we observe that there is a pathological class of
channels that admit trivial one-time programs without any hardware assumptions
whatsoever. We characterize these channels, assuming an interesting
conjecture on the invertible (or decoherence-free) subspaces of an arbitrary
channel.